Answer:
8159 W, 10.9 hp
Explanation:
The work done by the cheetah is equal to the kinetic energy gained, so we can write:
![W=\Delta K=\frac{1}{2}mv^2-\frac{1}{2}mu^2](https://tex.z-dn.net/?f=W%3D%5CDelta%20K%3D%5Cfrac%7B1%7D%7B2%7Dmv%5E2-%5Cfrac%7B1%7D%7B2%7Dmu%5E2)
where
m = 101 kg is the mass of the cheetah
u = 0 is the initial speed
v = 29.4 m/s is the final speed
Substituting,
![W=\frac{1}{2}(101)(29.4)^2-0=43650 J](https://tex.z-dn.net/?f=W%3D%5Cfrac%7B1%7D%7B2%7D%28101%29%2829.4%29%5E2-0%3D43650%20J)
Now we can calculate the power developed by the cheetah, given by:
![P=\frac{W}{t}](https://tex.z-dn.net/?f=P%3D%5Cfrac%7BW%7D%7Bt%7D)
where
t = 5.35 s
is the time taken. Substituting,
![P=\frac{43650}{5.35}=8159 W](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B43650%7D%7B5.35%7D%3D8159%20W)
And keeping in mind that
1 hp = 746 W
We can also convert into horsepowers:
![P=\frac{8159}{746}=10.9 hp](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B8159%7D%7B746%7D%3D10.9%20hp)